With an eye on uncertainty: Modelling pupillary responses to environmental volatility
Fig 8
Bayesian comparison of alternative models relative to the null model.
Fig 8a shows a bar plot of the log model evidence relative to that of the null model at a prior precision of 1, with the R2 scores for each fit provided above each bar (the lowest of our candidates, see Fig 9a). Fig 8b shows the posterior probabilities of the models, calculated by passing the log model evidence through a softmax function. In the case of Fig 8b, we take the model comparison conducted at a prior precision of β-1 = 2.25, to justify the model selected in the next section. Fig 8c shows the log model evidence for models 2–6 relative to that of model 1 (the null model), plotted against the prior belief over precision used to generate the design matrix for each mode, and can be thought of as a series of individual model comparisons. The curve for model 3 is in bold to indicate this is the model used for the analysis of participant’s prior beliefs. Note that the null model and models 5–6 do not depend on inferred precision and are therefore invariant to the prior beliefs. These results show that models explicitly containing inferred precision perform better over the range of prior beliefs considered, with the simpler model (model 3) performing best for β-1 > 2.25.